%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU598^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:31 AM UTC 2026
% Result : Theorem 1.63s 1.37s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 112 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 800 ( 212 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1043 ( 10 ~; 63 |; 20 &; 777 @)
% ( 0 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 10 con; 0-2 aty)
% ( 62 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 238 ( 75 ^; 157 !; 6 ?; 238 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_21,type,
sK3: $i > $i > $i ).
thf(f582,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f576,f27]) ).
thf(f27,plain,
( ( binintersect @ sK1 @ sK0 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( binintersectI = $true )
& ( binintersectRsub = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ( ( binintersect @ sK1 @ sK0 )
!= sK0 )
& ( $true
= ( subset @ sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
=> ( ( ( binintersect @ sK1 @ sK0 )
!= sK0 )
& ( $true
= ( subset @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( binintersectI = $true )
& ( binintersectRsub = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectRsub = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( setextsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectRsub = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X1 @ X0 )
= X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectRsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X1 @ X0 )
= X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectRsub
=> ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectRsub
=> ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',binintersectSubset4) ).
thf(f576,plain,
( ( binintersect @ sK1 @ sK0 )
= sK0 ),
inference(trivial_inequality_removal,[status(thm)],[f572]) ).
thf(f572,plain,
( ( $false = $true )
| ( ( binintersect @ sK1 @ sK0 )
= sK0 ) ),
inference(superposition,[status(thm)],[f86,f566]) ).
thf(f566,plain,
( ( subset @ sK0 @ ( binintersect @ sK1 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f565]) ).
thf(f565,plain,
( ( $false = $true )
| ( ( subset @ sK0 @ ( binintersect @ sK1 @ sK0 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f550]) ).
thf(f550,plain,
( ( ( subset @ sK0 @ ( binintersect @ sK1 @ sK0 ) )
= $true )
| ( $false = $true )
| ( ( subset @ sK0 @ ( binintersect @ sK1 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f309,f393]) ).
thf(f393,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK3 @ sK0 @ X0 ) @ sK1 ) )
| ( ( subset @ sK0 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f207,f373]) ).
thf(f373,plain,
! [X0: $i] :
( ( binintersect @ X0 @ X0 )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f363]) ).
thf(f363,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( binintersect @ X0 @ X0 )
= X0 ) ),
inference(superposition,[status(thm)],[f354,f86]) ).
thf(f354,plain,
! [X0: $i] :
( $true
= ( subset @ X0 @ ( binintersect @ X0 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f353]) ).
thf(f353,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( subset @ X0 @ ( binintersect @ X0 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f328]) ).
thf(f328,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( subset @ X0 @ ( binintersect @ X0 @ X0 ) ) )
| ( $true
= ( subset @ X0 @ ( binintersect @ X0 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f300,f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( $false
= ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f30,f25]) ).
thf(f25,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',subsetI1) ).
thf(f30,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f300,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X1 ) ) @ X1 ) )
| ( ( subset @ X0 @ ( binintersect @ X1 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f289]) ).
thf(f289,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X1 ) ) @ X1 ) )
| ( ( subset @ X0 @ ( binintersect @ X1 @ X1 ) )
= $true )
| ( $false != $false ) ),
inference(equality_factoring,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X2 ) )
| ( $true
= ( subset @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f160]) ).
thf(f160,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X1 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X2 ) )
| ( $true
= ( subset @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f68,f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X3 ) )
= $true )
| ( $false
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binintersect @ X1 @ X3 ) ) ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binintersect @ X1 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f35,f32]) ).
thf(f32,plain,
binintersectI = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f35,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( binintersectI
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',binintersectI) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f207,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ ( binintersect @ X0 @ sK0 ) @ X1 ) @ sK1 ) )
| ( ( subset @ ( binintersect @ X0 @ sK0 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f199]) ).
thf(f199,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ ( binintersect @ X0 @ sK0 ) @ X1 ) @ sK1 ) )
| ( $false = $true )
| ( ( subset @ ( binintersect @ X0 @ sK0 ) @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f69,f194]) ).
thf(f194,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binintersect @ X0 @ sK0 ) ) )
| ( ( in @ X1 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f190]) ).
thf(f190,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( in @ X1 @ sK1 )
= $true )
| ( $false
= ( in @ X1 @ ( binintersect @ X0 @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f60,f186]) ).
thf(f186,plain,
! [X0: $i] :
( $true
= ( subset @ ( binintersect @ X0 @ sK0 ) @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f185]) ).
thf(f185,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ sK0 ) @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f173]) ).
thf(f173,plain,
! [X0: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ sK0 ) @ sK1 ) )
| ( $false = $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ sK0 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f129,f146]) ).
thf(f146,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
= $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
= $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f69,f118]) ).
thf(f118,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $false ) ),
inference(superposition,[status(thm)],[f60,f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( subset @ ( binintersect @ X1 @ Y0 ) @ Y0 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( binintersect @ X1 @ Y0 ) @ Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( binintersect @ Y0 @ Y1 ) @ Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( binintersect @ Y0 @ Y1 ) @ Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f36,f31]) ).
thf(f31,plain,
binintersectRsub = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f36,plain,
( binintersectRsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( binintersect @ Y0 @ Y1 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( binintersectRsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( binintersect @ Y0 @ Y1 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= binintersectRsub ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= binintersectRsub ),
file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',binintersectRsub) ).
thf(f129,plain,
! [X0: $i] :
( ( ( in @ ( sK3 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( subset @ X0 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( subset @ X0 @ sK1 )
= $true )
| ( ( in @ ( sK3 @ X0 @ sK1 ) @ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f117,f68]) ).
thf(f117,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f26,f60]) ).
thf(f26,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X1 ) )
| ( $false
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) )
| ( $false
= ( subset @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f28]) ).
thf(f28,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f34,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X2 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetE
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',subsetE) ).
thf(f309,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X0 ) ) @ X1 ) )
| ( ( subset @ X0 @ ( binintersect @ X1 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f308]) ).
thf(f308,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X0 ) ) @ X1 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f282]) ).
thf(f282,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( $false = $true )
| ( $false
= ( in @ ( sK3 @ X0 @ ( binintersect @ X1 @ X0 ) ) @ X1 ) )
| ( ( subset @ X0 @ ( binintersect @ X1 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f69,f166]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( binintersect @ X0 @ X1 ) )
= $false )
| ( ( binintersect @ X0 @ X1 )
= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( binintersect @ X0 @ X1 ) )
= $false )
| ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f45,f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( ( subset @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $false )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) )
| ( $false
= ( subset @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f29]) ).
thf(f29,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f33,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',setextsub) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU598^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:28:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU598^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.29/0.46 % Version : Especial > Reduced > Especial.
% 0.29/0.46 % English : (! A:i.! B:i.subset B A -> binintersect A B = B)
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC100l [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 5 def)
% 0.29/0.46 % Number of atoms : 30 ( 7 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 7 ( 5 avg)
% 0.29/0.46 % Number of connectives : 46 ( 0 ~; 0 |; 0 &; 32 @)
% 0.29/0.46 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 11 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=365
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,conjecture,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( binintersectI
% 0.29/0.46 => ( binintersectRsub
% 0.29/0.46 => ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.63/1.31 ---- Embedded in THF ---
% 1.63/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.31 %%% Generated on Tue Feb 24 12:28:26 EST 2026
% 1.63/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.31 %%% Logic specification used:
% 1.63/1.31 %%% thf(spec, logic, $$dhol).
% 1.63/1.31
% 1.63/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2DTF6508.p
% See solution above
% 1.63/1.31 ------------------------
% 1.63/1.32 ---- Cleaned THF ---
% 1.63/1.32 thf(in_type,type,
% 1.63/1.32 in: $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(subset_type,type,
% 1.63/1.32 subset: $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(subsetI1_type,type,
% 1.63/1.32 subsetI1: $o ).
% 1.63/1.32
% 1.63/1.32 thf(subsetI1,definition,
% 1.63/1.32 ( subsetI1
% 1.63/1.32 = ( ! [A: $i,B: $i] :
% 1.63/1.32 ( ! [Xx: $i] :
% 1.63/1.32 ( ( in @ Xx @ A )
% 1.63/1.32 => ( in @ Xx @ B ) )
% 1.63/1.32 => ( subset @ A @ B ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(subsetE_type,type,
% 1.63/1.32 subsetE: $o ).
% 1.63/1.32
% 1.63/1.32 thf(subsetE,definition,
% 1.63/1.32 ( subsetE
% 1.63/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.63/1.32 ( ( subset @ A @ B )
% 1.63/1.32 => ( ( in @ Xx @ A )
% 1.63/1.32 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(setextsub_type,type,
% 1.63/1.32 setextsub: $o ).
% 1.63/1.32
% 1.63/1.32 thf(setextsub,definition,
% 1.63/1.32 ( setextsub
% 1.63/1.32 = ( ! [A: $i,B: $i] :
% 1.63/1.32 ( ( subset @ A @ B )
% 1.63/1.32 => ( ( subset @ B @ A )
% 1.63/1.32 => ( A = B ) ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(binintersect_type,type,
% 1.63/1.32 binintersect: $i > $i > $i ).
% 1.63/1.32
% 1.63/1.32 thf(binintersectI_type,type,
% 1.63/1.32 binintersectI: $o ).
% 1.63/1.32
% 1.63/1.32 thf(binintersectI,definition,
% 1.63/1.32 ( binintersectI
% 1.63/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.63/1.32 ( ( in @ Xx @ A )
% 1.63/1.32 => ( ( in @ Xx @ B )
% 1.63/1.32 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(binintersectRsub_type,type,
% 1.63/1.32 binintersectRsub: $o ).
% 1.63/1.32
% 1.63/1.32 thf(binintersectRsub,definition,
% 1.63/1.32 ( binintersectRsub
% 1.63/1.32 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(binintersectSubset4,conjecture,
% 1.63/1.32 ( subsetI1
% 1.63/1.32 => ( subsetE
% 1.63/1.32 => ( setextsub
% 1.63/1.32 => ( binintersectI
% 1.63/1.32 => ( binintersectRsub
% 1.63/1.32 => ! [A: $i,B: $i] :
% 1.63/1.32 ( ( subset @ B @ A )
% 1.63/1.32 => ( ( binintersect @ A @ B )
% 1.63/1.32 = B ) ) ) ) ) ) ) ).
% 1.63/1.32 ------------------------
% 1.63/1.34 % (6665)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/183Mi)
% 1.63/1.34 % (6668)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/2Mi)
% 1.63/1.34 % (6666)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/4Mi)
% 1.63/1.34 % (6668)Instruction limit reached!
% 1.63/1.34 % (6668)------------------------------
% 1.63/1.34 % (6668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (6668)Termination reason: Unknown
% 1.63/1.34 % (6668)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (6668)Memory used [KB]: 1023
% 1.63/1.34 % (6668)Time elapsed: 0.002 s
% 1.63/1.34 % (6668)Instructions burned: 3 (million)
% 1.63/1.34 % (6668)------------------------------
% 1.63/1.34 % (6668)------------------------------
% 1.63/1.34 % (6666)Instruction limit reached!
% 1.63/1.34 % (6666)------------------------------
% 1.63/1.34 % (6666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (6666)Termination reason: Unknown
% 1.63/1.34 % (6666)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (6666)Memory used [KB]: 5500
% 1.63/1.34 % (6666)Time elapsed: 0.003 s
% 1.63/1.34 % (6666)Instructions burned: 6 (million)
% 1.63/1.34 % (6666)------------------------------
% 1.63/1.34 % (6666)------------------------------
% 1.63/1.35 % (6667)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/27Mi)
% 1.63/1.35 % (6669)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/2Mi)
% 1.63/1.35 % (6671)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/18Mi)
% 1.63/1.35 % (6670)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/275Mi)
% 1.63/1.35 % (6669)Instruction limit reached!
% 1.63/1.35 % (6669)------------------------------
% 1.63/1.35 % (6669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (6669)Termination reason: Unknown
% 1.63/1.35 % (6669)Termination phase: Property scanning
% 1.63/1.35
% 1.63/1.35 % (6669)Memory used [KB]: 895
% 1.63/1.35 % (6669)Time elapsed: 0.003 s
% 1.63/1.35 % (6669)Instructions burned: 2 (million)
% 1.63/1.35 % (6669)------------------------------
% 1.63/1.35 % (6669)------------------------------
% 1.63/1.35 % (6672)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/3Mi)
% 1.63/1.35 % (6672)Instruction limit reached!
% 1.63/1.35 % (6672)------------------------------
% 1.63/1.35 % (6672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (6672)Termination reason: Unknown
% 1.63/1.35 % (6672)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (6672)Memory used [KB]: 5500
% 1.63/1.35 % (6672)Time elapsed: 0.002 s
% 1.63/1.35 % (6672)Instructions burned: 4 (million)
% 1.63/1.35 % (6672)------------------------------
% 1.63/1.35 % (6672)------------------------------
% 1.63/1.35 % (6673)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/37Mi)
% 1.63/1.36 % (6671)Instruction limit reached!
% 1.63/1.36 % (6671)------------------------------
% 1.63/1.36 % (6671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (6671)Termination reason: Unknown
% 1.63/1.36 % (6671)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (6671)Memory used [KB]: 5628
% 1.63/1.36 % (6671)Time elapsed: 0.014 s
% 1.63/1.36 % (6671)Instructions burned: 18 (million)
% 1.63/1.36 % (6671)------------------------------
% 1.63/1.36 % (6671)------------------------------
% 1.63/1.36 % (6675)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/3Mi)
% 1.63/1.36 % (6675)Instruction limit reached!
% 1.63/1.36 % (6675)------------------------------
% 1.63/1.36 % (6675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (6675)Termination reason: Unknown
% 1.63/1.36 % (6675)Termination phase: Property scanning
% 1.63/1.36
% 1.63/1.36 % (6675)Memory used [KB]: 1023
% 1.63/1.36 % (6675)Time elapsed: 0.002 s
% 1.63/1.36 % (6675)Instructions burned: 3 (million)
% 1.63/1.36 % (6675)------------------------------
% 1.63/1.36 % (6675)------------------------------
% 1.63/1.36 % (6667)Instruction limit reached!
% 1.63/1.36 % (6667)------------------------------
% 1.63/1.36 % (6667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (6667)Termination reason: Unknown
% 1.63/1.36 % (6667)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (6667)Memory used [KB]: 5628
% 1.63/1.36 % (6667)Time elapsed: 0.019 s
% 1.63/1.36 % (6667)Instructions burned: 27 (million)
% 1.63/1.36 % (6667)------------------------------
% 1.63/1.36 % (6667)------------------------------
% 1.63/1.36 % (6673)Instruction limit reached!
% 1.63/1.36 % (6673)------------------------------
% 1.63/1.36 % (6673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (6673)Termination reason: Unknown
% 1.63/1.36 % (6673)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (6673)Memory used [KB]: 5756
% 1.63/1.36 % (6673)Time elapsed: 0.015 s
% 1.63/1.36 % (6673)Instructions burned: 39 (million)
% 1.63/1.36 % (6673)------------------------------
% 1.63/1.36 % (6673)------------------------------
% 1.63/1.36 % (6674)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/15Mi)
% 1.63/1.36 % (6665)First to succeed.
% 1.63/1.37 % (6665)Refutation found. Thanks to Tanya!
% 1.63/1.37 % SZS status Theorem for DTF2THF_6508
% 1.63/1.37 % SZS output start Proof for DTF2THF_6508
% 1.63/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.63/1.37 thf(func_def_1, type, subset: $i > $i > $o).
% 1.63/1.37 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.63/1.37 thf(func_def_21, type, sK3: $i > $i > $i).
% 1.63/1.37 thf(f582,plain,(
% 1.63/1.37 $false),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f576,f27])).
% 1.63/1.37 thf(f27,plain,(
% 1.63/1.37 ((binintersect @ sK1 @ sK0) != sK0)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f24,plain,(
% 1.63/1.37 (binintersectI = $true) & (binintersectRsub = $true) & (subsetI1 = $true) & (setextsub = $true) & (subsetE = $true) & (((binintersect @ sK1 @ sK0) != sK0) & ($true = (subset @ sK0 @ sK1)))),
% 1.63/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f23])).
% 1.63/1.37 thf(f23,plain,(
% 1.63/1.37 ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)) => (((binintersect @ sK1 @ sK0) != sK0) & ($true = (subset @ sK0 @ sK1)))),
% 1.63/1.37 introduced(definition,[],[choice_axiom])).
% 1.63/1.37 thf(f22,plain,(
% 1.63/1.37 (binintersectI = $true) & (binintersectRsub = $true) & (subsetI1 = $true) & (setextsub = $true) & (subsetE = $true) & ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true))),
% 1.63/1.37 inference(flattening,[status(thm)],[f21])).
% 1.63/1.37 thf(f21,plain,(
% 1.63/1.37 ((((? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)) & (binintersectRsub = $true)) & (binintersectI = $true)) & (setextsub = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 1.63/1.37 inference(ennf_transformation,[status(thm)],[f16])).
% 1.63/1.37 thf(f16,plain,(
% 1.63/1.37 ~((subsetI1 = $true) => ((subsetE = $true) => ((setextsub = $true) => ((binintersectI = $true) => ((binintersectRsub = $true) => ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X1 @ X0) = X0)))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f15])).
% 1.63/1.37 thf(f15,plain,(
% 1.63/1.37 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectRsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X1 @ X0) = X0)))))))),
% 1.63/1.37 inference(rectify,[status(thm)],[f7])).
% 1.63/1.37 thf(f7,negated_conjecture,(
% 1.63/1.37 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectRsub => ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)))))))),
% 1.63/1.37 inference(negated_conjecture,[status(cth)],[f6])).
% 1.63/1.37 thf(f6,conjecture,(
% 1.63/1.37 subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectRsub => ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1))))))),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',binintersectSubset4)).
% 1.63/1.37 thf(f576,plain,(
% 1.63/1.37 ((binintersect @ sK1 @ sK0) = sK0)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f572])).
% 1.63/1.37 thf(f572,plain,(
% 1.63/1.37 ($false = $true) | ((binintersect @ sK1 @ sK0) = sK0)),
% 1.63/1.37 inference(superposition,[status(thm)],[f86,f566])).
% 1.63/1.37 thf(f566,plain,(
% 1.63/1.37 ((subset @ sK0 @ (binintersect @ sK1 @ sK0)) = $true)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f565])).
% 1.63/1.37 thf(f565,plain,(
% 1.63/1.37 ($false = $true) | ((subset @ sK0 @ (binintersect @ sK1 @ sK0)) = $true)),
% 1.63/1.37 inference(duplicate_literal_removal,[status(thm)],[f550])).
% 1.63/1.37 thf(f550,plain,(
% 1.63/1.37 ((subset @ sK0 @ (binintersect @ sK1 @ sK0)) = $true) | ($false = $true) | ((subset @ sK0 @ (binintersect @ sK1 @ sK0)) = $true)),
% 1.63/1.37 inference(superposition,[status(thm)],[f309,f393])).
% 1.63/1.37 thf(f393,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($true = (in @ (sK3 @ sK0 @ X0) @ sK1)) | ((subset @ sK0 @ X0) = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f207,f373])).
% 1.63/1.37 thf(f373,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (((binintersect @ X0 @ X0) = X0)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f363])).
% 1.63/1.37 thf(f363,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($false = $true) | ((binintersect @ X0 @ X0) = X0)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f354,f86])).
% 1.63/1.37 thf(f354,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($true = (subset @ X0 @ (binintersect @ X0 @ X0)))) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 1.63/1.37 thf(f353,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($false = $true) | ($true = (subset @ X0 @ (binintersect @ X0 @ X0)))) )),
% 1.63/1.37 inference(duplicate_literal_removal,[status(thm)],[f328])).
% 1.63/1.37 thf(f328,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($false = $true) | ($true = (subset @ X0 @ (binintersect @ X0 @ X0))) | ($true = (subset @ X0 @ (binintersect @ X0 @ X0)))) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f300,f69])).
% 1.63/1.37 thf(f69,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK3 @ X1 @ X2) @ X1)) | ((subset @ X1 @ X2) = $true)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.63/1.37 thf(f67,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (((subset @ X1 @ X2) = $true) | ($false = ((in @ (sK3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X1 @ X2) @ X2)))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.63/1.37 thf(f66,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK3 @ X1 @ X2)) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.63/1.37 inference(sigma_clausification,[status(thm)],[f65])).
% 1.63/1.37 thf(f65,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (((subset @ X1 @ X2) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.63/1.37 thf(f64,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.63/1.37 thf(f63,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f62])).
% 1.63/1.37 thf(f62,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.63/1.37 thf(f61,plain,(
% 1.63/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f37])).
% 1.63/1.37 thf(f37,plain,(
% 1.63/1.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) = $true)),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f30,f25])).
% 1.63/1.37 thf(f25,plain,(
% 1.63/1.37 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.37 thf(f12,plain,(
% 1.63/1.37 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f11])).
% 1.63/1.37 thf(f11,plain,(
% 1.63/1.37 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 1.63/1.37 inference(rectify,[status(thm)],[f1])).
% 1.63/1.37 thf(f1,axiom,(
% 1.63/1.37 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',subsetI1)).
% 1.63/1.37 thf(f30,plain,(
% 1.63/1.37 (subsetI1 = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f300,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X1)) @ X1)) | ((subset @ X0 @ (binintersect @ X1 @ X1)) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f289])).
% 1.63/1.37 thf(f289,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X1)) @ X1)) | ((subset @ X0 @ (binintersect @ X1 @ X1)) = $true) | ($false != $false)) )),
% 1.63/1.37 inference(equality_factoring,[status(thm)],[f166])).
% 1.63/1.37 thf(f166,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X2)) @ X2)) | ($true = (subset @ X0 @ (binintersect @ X1 @ X2))) | ($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X2)) @ X1))) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f160])).
% 1.63/1.37 thf(f160,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X2)) @ X1)) | ($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X2)) @ X2)) | ($true = (subset @ X0 @ (binintersect @ X1 @ X2))) | ($false = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f68,f77])).
% 1.63/1.37 thf(f77,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X1 @ X3)) = $true) | ($false = (in @ X2 @ X3)) | ((in @ X2 @ X1) = $false)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.63/1.37 thf(f76,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => (in @ X2 @ (binintersect @ X1 @ X3)))) | ((in @ X2 @ X1) = $false)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.63/1.37 thf(f75,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => ((in @ X2 @ X3) => (in @ X2 @ (binintersect @ X1 @ X3)))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.63/1.37 thf(f74,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ X2 @ Y0) => (in @ X2 @ (binintersect @ X1 @ Y0))))) @ X3) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f73])).
% 1.63/1.37 thf(f73,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ X2 @ Y0) => (in @ X2 @ (binintersect @ X1 @ Y0)))))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.63/1.37 thf(f72,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ X1 @ Y1))))))) @ X2))) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f71])).
% 1.63/1.37 thf(f71,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ X1 @ Y1)))))))) = $true)) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.63/1.37 thf(f70,plain,(
% 1.63/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ (binintersect @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f40])).
% 1.63/1.37 thf(f40,plain,(
% 1.63/1.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) = $true)),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f35,f32])).
% 1.63/1.37 thf(f32,plain,(
% 1.63/1.37 (binintersectI = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f35,plain,(
% 1.63/1.37 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.63/1.37 thf(f18,plain,(
% 1.63/1.37 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f17])).
% 1.63/1.37 thf(f17,plain,(
% 1.63/1.37 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ (binintersect @ X2 @ X0)))))),
% 1.63/1.37 inference(rectify,[status(thm)],[f4])).
% 1.63/1.37 thf(f4,axiom,(
% 1.63/1.37 (binintersectI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',binintersectI)).
% 1.63/1.37 thf(f68,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK3 @ X1 @ X2) @ X2)) | ((subset @ X1 @ X2) = $true)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.63/1.37 thf(f207,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK3 @ (binintersect @ X0 @ sK0) @ X1) @ sK1)) | ((subset @ (binintersect @ X0 @ sK0) @ X1) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f199])).
% 1.63/1.37 thf(f199,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK3 @ (binintersect @ X0 @ sK0) @ X1) @ sK1)) | ($false = $true) | ((subset @ (binintersect @ X0 @ sK0) @ X1) = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f69,f194])).
% 1.63/1.37 thf(f194,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($false = (in @ X1 @ (binintersect @ X0 @ sK0))) | ((in @ X1 @ sK1) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f190])).
% 1.63/1.37 thf(f190,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((in @ X1 @ sK1) = $true) | ($false = (in @ X1 @ (binintersect @ X0 @ sK0)))) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f60,f186])).
% 1.63/1.37 thf(f186,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($true = (subset @ (binintersect @ X0 @ sK0) @ sK1))) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f185])).
% 1.63/1.37 thf(f185,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($false = $true) | ($true = (subset @ (binintersect @ X0 @ sK0) @ sK1))) )),
% 1.63/1.37 inference(duplicate_literal_removal,[status(thm)],[f173])).
% 1.63/1.37 thf(f173,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($true = (subset @ (binintersect @ X0 @ sK0) @ sK1)) | ($false = $true) | ($true = (subset @ (binintersect @ X0 @ sK0) @ sK1))) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f129,f146])).
% 1.63/1.37 thf(f146,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ (binintersect @ X0 @ X1) @ X2) @ X1) = $true) | ((subset @ (binintersect @ X0 @ X1) @ X2) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.63/1.37 thf(f144,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ (binintersect @ X0 @ X1) @ X2) @ X1) = $true) | ((subset @ (binintersect @ X0 @ X1) @ X2) = $true) | ($false = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f69,f118])).
% 1.63/1.37 thf(f118,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $false) | ((in @ X2 @ X1) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.63/1.37 thf(f109,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) = $false)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f60,f45])).
% 1.63/1.37 thf(f45,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X2) = $true)) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.63/1.37 thf(f44,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (subset @ (binintersect @ X1 @ Y0) @ Y0)) @ X2) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f43])).
% 1.63/1.37 thf(f43,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (subset @ (binintersect @ X1 @ Y0) @ Y0))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.63/1.37 thf(f42,plain,(
% 1.63/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1)))) @ X1) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f41])).
% 1.63/1.37 thf(f41,plain,(
% 1.63/1.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) = $true)),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f36,f31])).
% 1.63/1.37 thf(f31,plain,(
% 1.63/1.37 (binintersectRsub = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f36,plain,(
% 1.63/1.37 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.37 thf(f14,plain,(
% 1.63/1.37 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f13])).
% 1.63/1.37 thf(f13,plain,(
% 1.63/1.37 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X0) = binintersectRsub)),
% 1.63/1.37 inference(rectify,[status(thm)],[f5])).
% 1.63/1.37 thf(f5,axiom,(
% 1.63/1.37 (! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1) = binintersectRsub)),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',binintersectRsub)).
% 1.63/1.37 thf(f129,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (((in @ (sK3 @ X0 @ sK1) @ sK0) = $false) | ((subset @ X0 @ sK1) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.63/1.37 thf(f126,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($false = $true) | ((subset @ X0 @ sK1) = $true) | ((in @ (sK3 @ X0 @ sK1) @ sK0) = $false)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f117,f68])).
% 1.63/1.37 thf(f117,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($true = (in @ X0 @ sK1)) | ((in @ X0 @ sK0) = $false)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.63/1.37 thf(f110,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($false = $true) | ($true = (in @ X0 @ sK1)) | ((in @ X0 @ sK0) = $false)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f26,f60])).
% 1.63/1.37 thf(f26,plain,(
% 1.63/1.37 ($true = (subset @ sK0 @ sK1))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f60,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X3 @ X1)) | ($false = (in @ X2 @ X3)) | ((in @ X2 @ X1) = $true)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.63/1.37 thf(f59,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => (in @ X2 @ X1))) | ($false = (subset @ X3 @ X1))) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.63/1.37 thf(f58,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X3 @ X1) => ((in @ X2 @ X3) => (in @ X2 @ X1))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.63/1.37 thf(f57,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ X1) => ((in @ X2 @ Y0) => (in @ X2 @ X1)))) @ X3))) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f56])).
% 1.63/1.37 thf(f56,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => ((in @ X2 @ Y0) => (in @ X2 @ X1))))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.63/1.37 thf(f55,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ X1) => ((in @ Y0 @ Y1) => (in @ Y0 @ X1)))))) @ X2) = $true)) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f54])).
% 1.63/1.37 thf(f54,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ X1) => ((in @ Y0 @ Y1) => (in @ Y0 @ X1))))))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.63/1.37 thf(f53,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))) @ X1))) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f39])).
% 1.63/1.37 thf(f39,plain,(
% 1.63/1.37 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f34,f28])).
% 1.63/1.37 thf(f28,plain,(
% 1.63/1.37 (subsetE = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f34,plain,(
% 1.63/1.37 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f20])).
% 1.63/1.37 thf(f20,plain,(
% 1.63/1.37 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f19])).
% 1.63/1.37 thf(f19,plain,(
% 1.63/1.37 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))))),
% 1.63/1.37 inference(rectify,[status(thm)],[f2])).
% 1.63/1.37 thf(f2,axiom,(
% 1.63/1.37 (subsetE = ! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',subsetE)).
% 1.63/1.37 thf(f309,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X0)) @ X1)) | ((subset @ X0 @ (binintersect @ X1 @ X0)) = $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f308])).
% 1.63/1.37 thf(f308,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X1 @ X0)) = $true) | ($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X0)) @ X1)) | ($false = $true)) )),
% 1.63/1.37 inference(duplicate_literal_removal,[status(thm)],[f282])).
% 1.63/1.37 thf(f282,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X1 @ X0)) = $true) | ($false = $true) | ($false = (in @ (sK3 @ X0 @ (binintersect @ X1 @ X0)) @ X1)) | ((subset @ X0 @ (binintersect @ X1 @ X0)) = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f69,f166])).
% 1.63/1.37 thf(f86,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (binintersect @ X0 @ X1)) = $false) | ((binintersect @ X0 @ X1) = X1)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.63/1.37 thf(f81,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (binintersect @ X0 @ X1)) = $false) | ((binintersect @ X0 @ X1) = X1) | ($false = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f45,f52])).
% 1.63/1.37 thf(f52,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (subset @ X2 @ X1)) | ((subset @ X1 @ X2) = $false) | (X1 = X2)) )),
% 1.63/1.37 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.63/1.37 thf(f51,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (((subset @ X1 @ X2) = $false) | ($false = (subset @ X2 @ X1)) | ($true = (X2 = X1))) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.63/1.37 thf(f50,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X1 @ X2) => (X2 = X1))) | ($false = (subset @ X2 @ X1))) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.63/1.37 thf(f49,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X2 @ X1) => ((subset @ X1 @ X2) => (X2 = X1))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.63/1.37 thf(f48,plain,(
% 1.63/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1)))) @ X2))) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f47])).
% 1.63/1.37 thf(f47,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1))))))) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.63/1.37 thf(f46,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0)))))) @ X1))) )),
% 1.63/1.37 inference(pi_clausification,[status(thm)],[f38])).
% 1.63/1.37 thf(f38,plain,(
% 1.63/1.37 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f33,f29])).
% 1.63/1.37 thf(f29,plain,(
% 1.63/1.37 (setextsub = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.37 thf(f33,plain,(
% 1.63/1.37 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.37 thf(f10,plain,(
% 1.63/1.37 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f9])).
% 1.63/1.37 thf(f9,plain,(
% 1.63/1.37 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.63/1.37 inference(rectify,[status(thm)],[f3])).
% 1.63/1.37 thf(f3,axiom,(
% 1.63/1.37 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.qc5xu6Xbn0/DTF2THF_6508.p',setextsub)).
% 1.63/1.37 % SZS output end Proof for DTF2THF_6508
% 1.63/1.37 % (6665)------------------------------
% 1.63/1.37 % (6665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (6665)Termination reason: Refutation
% 1.63/1.37
% 1.63/1.37 % (6665)Memory used [KB]: 6012
% 1.63/1.37 % (6665)Time elapsed: 0.031 s
% 1.63/1.37 % (6665)Instructions burned: 86 (million)
% 1.63/1.37 % (6665)------------------------------
% 1.63/1.37 % (6665)------------------------------
% 1.63/1.37 % (6664)Success in time 0.029 s
%------------------------------------------------------------------------------